Advance Biostats SPSS (Multiple Linear Regression)

PART2

Step-by-Step Guide Assignment Problem 4.2

Multivariate Linear Regression

Problem 2. Conduct a multiple linear regression using SPSS. Provide relevant SPSS output and assess the statistical significance of the effects of mother’s Age, BMI, and Coffee (Cups per Day) on Birth weight.

Step 1. Go to Analyze ( Regression ( Linear.

Step 2. Transfer “birthw” to the Dependent box. Transfer “age”, “bmi”, and “coffee” to the Independent(s) box. Click Statistics

Step 3. In the Linear Regression: Statistics window, check Estimates, Confidence intervals Level(%) 95, and Model fit. Click continue. Click OK.

SPSS Output:

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.579a	.336	.313	386.671
a. Predictors: (Constant), cups per day, body mass index, age at conception
Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	95.0% Confidence Interval for B
	B	Std. Error	Beta			Lower Bound	Upper Bound
1	(Constant)	1660.890	335.521		4.950	.000	994.004	2327.775
	age at conception	44.481	8.639	.458	5.149	.000	27.310	61.653
	body mass index	32.683	9.214	.311	3.547	.001	14.369	50.997
	cups per day	-46.995	16.769	-.250	-2.802	.006	-80.325	-13.664
a. Dependent Variable: birth weight

Discussion:

Model Summary table:

The value of R tells you the direction (positive or negative) and strength (0 = no correlation, 1 = perfect correlation) of the association between all independent variables and the dependent variable.

R square is called the coefficient of determination. It tells you how much of the variability in the dependent variable can be explained by regression on the independent variables. Stated differently, R square explains how much of the differences between the dependent values are due to the independent variables in your model. For example, an R square of 0.924 means that 92% of the variation in a dependent variable is due to the independent variables tested in the logistic regression.

Coefficients table:

Under Beta (β), there will be a value for the constant (Constant) representing the y-intercept and an additional value under the y-intercept for each independent variable in the model. The β adjacent to each independent variable represents the amount of change in the dependent variable for each 1 unit change in the independent variable while all other variables in the model are held constant.

A positive β means the association between the independent and dependent variables is positive - for each unit increase in the independent variable, there is β increase in the dependent variable.

A negative β means the association between independent and dependent variables is negative or inverse for each unit increase in the independent variable, there is β decrease in the dependent variable.

Sig. provides the p-value for the change (< 0.05 is significant).

Interpretation for this problem:

In this section you must discuss:

1. What the value of R tells you about the association between variables included in the model and your dependent variable.

2. What is the meaning of R square in your output?

3. What is the meaning of the Beta coefficients for each independent variable?

4. What a positive and negative Beta coefficient means?

5. What is the meaning of the significance levels in your table?

6. What are your general conclusions about this regression model?